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Chebyshev polynomials and Pell equations over finite fields

Boaz Cohen (2021)

Czechoslovak Mathematical Journal

We shall describe how to construct a fundamental solution for the Pell equation x 2 - m y 2 = 1 over finite fields of characteristic p 2 . Especially, a complete description of the structure of these fundamental solutions will be given using Chebyshev polynomials. Furthermore, we shall describe the structure of the solutions of the general Pell equation x 2 - m y 2 = n .

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